How does time to run Ward's vs PAM vs DIANA clustering differ with scale?

We will test this using sequence objects with 1,000, 2,000, and 4,000 members for Ward's and PAM. For DIANA, we will test a 4,000 member sample for all possible properties.

Definitions

WeightedCluster Manual

Create sequence objects

set.seed(09112020)

sts_nonvet <- read.csv("~/git/DSPG2020/career/data/sts_all_ten.csv", row.names = 1)

small <- sts_nonvet[sample(nrow(sts_nonvet), 1000, replace = FALSE, prob = NULL),]
medium <- sts_nonvet[sample(nrow(sts_nonvet), 2000, replace = FALSE, prob = NULL),]
large <- sts_nonvet[sample(nrow(sts_nonvet), 4000, replace = FALSE, prob = NULL),]

small <- seqdef(small, left="DEL", gaps="Civilian unemployment", right="DEL", cpal = c("#CBBEB5",  uva_color_palette[1], uva_color_palette[2],uva_color_palette[4],  uva_color_palette[6], uva_color_palette[9], "#CBBEB5"))

medium <- seqdef(medium, left="DEL", gaps="Civilian unemployment", right="DEL", cpal = c("#CBBEB5",  uva_color_palette[1], uva_color_palette[2],uva_color_palette[4],  uva_color_palette[6], uva_color_palette[9], "#CBBEB5"))

large <- seqdef(large, left="DEL", gaps="Civilian unemployment", right="DEL", cpal = c("#CBBEB5",  uva_color_palette[1], uva_color_palette[2],uva_color_palette[4],  uva_color_palette[6], uva_color_palette[9], "#CBBEB5"))

Our sample data comes from a sample of nonveterans who have at least ten years of employment history. We will cluster based on the whole sequence and in exploratory plots limit the axis to the first 30 years of employment history.

1,000 member clustering

reps = 1:10
diss <- seqdist(small, method = "OM", indel = 1, sm = "TRATE", with.missing = TRUE)

cluster_times <- for(rep in reps) {
rep = as.character(rep)

# Ward's clustering
start_w <- Sys.time()
clusterward <- agnes(diss, diss = TRUE, method = "ward")
end_w <- Sys.time()
assign(paste0("w_run_", rep), (end_w - start_w), envir = .GlobalEnv)

# PAM clustering
start_p <- Sys.time()
clusterpam <- wcKMedoids(diss, k = 8)
end_p <- Sys.time()
assign(paste0("p_run_", rep), (end_p - start_p), envir = .GlobalEnv)

assign("clusterward_s", clusterward, envir = .GlobalEnv)
assign("clusterpam_s", clusterpam, envir = .GlobalEnv)
}

small_w_time <- mean.difftime((w_run_1 + w_run_2 + w_run_3 + w_run_4 + w_run_5 + w_run_6 + w_run_7 + w_run_8 + w_run_9 + w_run_10)/10)

small_p_time <- mean.difftime((p_run_1 + p_run_2 + p_run_3 + p_run_4 + p_run_5 + p_run_6 + p_run_7 + p_run_8 + p_run_9 + p_run_10)/10)

small_w_time
## Time difference of 0.7419001 secs
small_p_time
## Time difference of 0.3111416 secs

In small samples PAM is about twice as fast.

2,000 member clustering

# Normal clustering

reps = 1:5
diss <- seqdist(medium, method = "OM", indel = 1, sm = "TRATE", with.missing = TRUE)

cluster_times <- for(rep in reps) {
rep = as.character(rep)

# Ward's cluster
start_w <- Sys.time()
clusterward <- agnes(diss, diss = TRUE, method = "ward")
end_w <- Sys.time()
assign(paste0("w_run_", rep), (end_w - start_w), envir = .GlobalEnv)

# PAM cluster
start_p <- Sys.time()
clusterpam <- wcKMedoids(diss, k = 8)
end_p <- Sys.time()
assign(paste0("p_run_", rep), (end_p - start_p), envir = .GlobalEnv)

assign("clusterward_m", clusterward, envir = .GlobalEnv)
assign("clusterpam_m", clusterpam, envir = .GlobalEnv)
}

medium_w_time <- mean.difftime((w_run_1 + w_run_2 + w_run_3 + w_run_4 + w_run_5)/5)

medium_p_time <- mean.difftime((p_run_1 + p_run_2 + p_run_3 + p_run_4 + p_run_5)/5)

medium_w_time
## Time difference of 6.165188 secs
medium_p_time
## Time difference of 1.673087 secs

In medium samples PAM is about twice as fast.

4,000 member clustering

# Normal clustering

reps = 3
diss <- seqdist(large, method = "OM", indel = 1, sm = "TRATE", with.missing = TRUE)

cluster_times <- for (rep in reps) {
rep = as.character(rep)
  
start_w <- Sys.time()
clusterward <- agnes(diss, diss = TRUE, method = "ward")
end_w <- Sys.time()
assign(paste0("w_run_", rep), (end_w - start_w), envir = .GlobalEnv)

# Weighted clustering
start_p <- Sys.time()
clusterpam <- wcKMedoids(diss, k = 8)
end_p <- Sys.time()
assign(paste0("p_run_", rep), (end_p - start_p), envir = .GlobalEnv)

assign("clusterward_l", clusterward, envir = .GlobalEnv)
assign("clusterpam_l", clusterpam, envir = .GlobalEnv)
}

large_w_time <- mean.difftime((w_run_1 + w_run_2 + w_run_3)/3)

large_p_time <- mean.difftime((p_run_1 + w_run_2 + p_run_3)/3)

large_w_time
## Time difference of 34.42106 secs
large_p_time
## Time difference of 5.199043 secs

In large samples PAM is more than twice as fast.

Time table

times <- tibble("type" = c("unweighted", "weighted"),
                "1000" = c(small_w_time, small_p_time),
                "2000" = c(medium_w_time, medium_p_time),
                "4000" = c(large_w_time, large_p_time))

times
## # A tibble: 2 x 4
##   type       `1000`         `2000`        `4000`        
##   <chr>      <drtn>         <drtn>        <drtn>        
## 1 unweighted 0.7419001 secs 6.165188 secs 34.421057 secs
## 2 weighted   0.3111416 secs 1.673087 secs  5.199043 secs

Overall PAM is faster than Ward's at all levels, with the difference increasing as the sample size increases. Though even the "large" sample runs for both methods in under a minute, it is important to remember we are interested in clustering sequence objects with 40,000+ members.

(Assuming no differences in the cluster outputs) Because of the flexible nature of Ward's clustering (number of clusters selected after clustering), it may be advantageous to perform exploratory analysis to decide number of clusters on a small sample using Ward's method before clustering the whole object with PAM.

Cluster differences

# small clusters
clusterward_8 <- cutree(clusterward_s, k = 8)
clusterward_8_fac <- factor(clusterward_8, labels = paste("Type", 1:8))

clusterpam_8 <- clusterpam_s$clustering
clusterpam_8_fac <- factor(clusterpam_8, labels = paste("Type", 1:8))

clusterpam_8_fac <- factor(clusterpam_8_fac, levels = c("Type 2", "Type 8", "Type 3", "Type 7", "Type 4", "Type 5", "Type 1", "Type 6"))

par(mfrow=c(1,3))
w_plot <- seqIplot(small[,1:30], group = clusterward_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "wards")

p_plot <- seqIplot(small[,1:30], group = clusterpam_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "pam")

seqlegend(small)

as.data.frame(clusterward_8_fac) %>%
  group_by(clusterward_8_fac) %>% summarise(n = n())
## # A tibble: 8 x 2
##   clusterward_8_fac     n
##   <fct>             <int>
## 1 Type 1               71
## 2 Type 2              343
## 3 Type 3              122
## 4 Type 4              155
## 5 Type 5              137
## 6 Type 6               75
## 7 Type 7               61
## 8 Type 8               36
as.data.frame(clusterpam_8_fac) %>%
  group_by(clusterpam_8_fac) %>% summarise(n = n()) 
## # A tibble: 8 x 2
##   clusterpam_8_fac     n
##   <fct>            <int>
## 1 Type 2             155
## 2 Type 8              75
## 3 Type 3              85
## 4 Type 7              78
## 5 Type 4             196
## 6 Type 5             103
## 7 Type 1             174
## 8 Type 6             134
# medium clusters
clusterward_8 <- cutree(clusterward_m, k = 8)
clusterward_8_fac <- factor(clusterward_8, labels = paste("Type", 1:8))

clusterpam_8 <- clusterpam_m$clustering
clusterpam_8_fac <- factor(clusterpam_8, labels = paste("Type", 1:8))

clusterpam_8_fac <- factor(clusterpam_8_fac, levels = c("Type 2", "Type 8", "Type 3", "Type 7", "Type 4", "Type 5", "Type 1", "Type 6"))

par(mfrow=c(1,3))

w_plot <- seqIplot(medium[,1:30], group = clusterward_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "wards")

p_plot <- seqIplot(medium[,1:30], group = clusterpam_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "pam")

seqlegend(medium)

as.data.frame(clusterward_8_fac) %>%
  group_by(clusterward_8_fac) %>% summarise(n = n())
## # A tibble: 8 x 2
##   clusterward_8_fac     n
##   <fct>             <int>
## 1 Type 1              494
## 2 Type 2              196
## 3 Type 3              293
## 4 Type 4               74
## 5 Type 5              281
## 6 Type 6              291
## 7 Type 7              196
## 8 Type 8              175
as.data.frame(clusterpam_8_fac) %>%
  group_by(clusterpam_8_fac) %>% summarise(n = n()) 
## # A tibble: 8 x 2
##   clusterpam_8_fac     n
##   <fct>            <int>
## 1 Type 2             240
## 2 Type 8             329
## 3 Type 3             157
## 4 Type 7             228
## 5 Type 4             434
## 6 Type 5             140
## 7 Type 1             310
## 8 Type 6             162
# large clusters
clusterward_8 <- cutree(clusterward, k = 8)
clusterward_8_fac <- factor(clusterward_8, labels = paste("Type", 1:8))

clusterpam_8 <- clusterpam$clustering
clusterpam_8_fac <- factor(clusterpam_8, labels = paste("Type", 1:8))

clusterpam_8_fac <- factor(clusterpam_8_fac, levels = c("Type 2", "Type 8", "Type 3", "Type 7", "Type 4", "Type 5", "Type 1", "Type 6"))

par(mfrow=c(1,3))

w_plot <- seqIplot(large[,1:30], group = clusterward_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "wards")

p_plot <- seqIplot(large[,1:30], group = clusterpam_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "pam")

seqlegend(large)

as.data.frame(clusterward_8_fac) %>%
  group_by(clusterward_8_fac) %>% summarise(n = n())
## # A tibble: 8 x 2
##   clusterward_8_fac     n
##   <fct>             <int>
## 1 Type 1              926
## 2 Type 2              610
## 3 Type 3              350
## 4 Type 4              588
## 5 Type 5              624
## 6 Type 6              493
## 7 Type 7              143
## 8 Type 8              266
as.data.frame(clusterpam_8_fac) %>%
  group_by(clusterpam_8_fac) %>% summarise(n = n()) 
## # A tibble: 8 x 2
##   clusterpam_8_fac     n
##   <fct>            <int>
## 1 Type 2             549
## 2 Type 8             857
## 3 Type 3             276
## 4 Type 7             339
## 5 Type 4             316
## 6 Type 5             417
## 7 Type 1             537
## 8 Type 6             709

Overall the clusters look pretty similar. The biggest differences are the Ward's solution has two unemployment clusters. The PAM solution has a career mobility cluster (Type 3). Surprisingly, the PAM cluster solution has a more even distribution (523 range) than the Ward's (885 range) solution.

The similar cluster outputs support choosing Ward's or PAM clustering based on desired efficiency in flexibility in the number of clusters or a quicker runtime varying with sample size. It is likely that choosing a specific dissimilarity metric or performing DIANA clustering will have a greater impact on the cluster outputs.

DIANA clustering

The creators of the TraMineR and WeightedCluster package have created tools to implement monothetic divise clustering of sequences in R (https://link.springer.com/chapter/10.1007/978-3-319-95420-2_13). This type of clustering is reffered to as property based clustering, as it gives us more control over the specific properties of sequences used to create clusters.

  • state: The state in which an individual is found, at each time position t
  • spell.age: The age at the beginning of each spell of a given type
  • spell.dur: The duration of each of the spells presented above
  • duration: The total time spent in each state
  • pattern: Count of the frequent subsequences of states in the distinct successive states
  • AFpattern: Age at the first occurrence of the above frequent subsequence
  • transition: Count of the frequent subsequence of events in each sequence, where each transition is considered another event
  • AFtransition: Age at the first occurrence of the above frequent subsequence
  • Complexity: Complexity index, number of transitions, turbulence

Here we test the speed of clustering by each of these properties with the large subset.

properties <- c("state", "spell.age", "spell.dur", "duration", "pattern", "AFpattern", "transition", "AFtransition", "Complexity")

for (property in properties) {
start_prop <- Sys.time()
clusterprop <- seqpropclust(large, diss = diss, properties = property, maxcluster = 8)
end_prop <- Sys.time()

clusterprop_8 <- clusterprop$fitted
clusterprop_10_fac <- factor(clusterprop_8$`(fitted)`, labels = paste("Type", 1:8))

prop_plot <- seqIplot(large[,1:30], group = clusterprop_10_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = property)

assign(paste0("clusterprop", property), clusterprop, envir = .GlobalEnv)
assign(paste0("prop_run_", property), (end_prop - start_prop), envir = .GlobalEnv)
assign(property, prop_plot, envir = .GlobalEnv)
}

prop_run_state
## Time difference of 5.401265 secs
prop_run_spell.age
## Time difference of 3.215952 secs
prop_run_spell.dur
## Time difference of 3.322732 secs
prop_run_duration
## Time difference of 1.226229 secs
prop_run_pattern
## Time difference of 6.725509 secs
prop_run_AFpattern
## Time difference of 8.913283 secs
prop_run_transition
## Time difference of 4.217427 secs
prop_run_AFtransition
## Time difference of 4.785521 secs
prop_run_Complexity
## Time difference of 3.452164 mins
prop_time <- mean.difftime((prop_run_state + prop_run_spell.age + prop_run_spell.dur + prop_run_duration + prop_run_pattern + prop_run_AFpattern + prop_run_transition + prop_run_AFtransition + prop_run_Complexity)/9)

prop_time
## Time difference of 27.2153 secs

state: The state in which an individual is found, at each time position t Clustered by state in early, mid, and late career. Clusters 1 and 2 are Zone 4 early career, Cluster 3 is Zone 4 mid career. Cluster 4 is Zone 3 early career. Cluster 5 is Zone 3 mid career. Cluster 6 is Zone 2 mid career. Cluster 7 is zone 5 mid career. Cluster 8 is missing/unemployed mid career. Pretty similar to PAM and Wards Solutions

spell.age: The age at the beginning of each spell of a given type I think these are emphasizing the relationships between subsequence or two states. Type 1 is Zone 4 and Zone 3, Type 2 is Zone 4 and Unemployment/Missing, Type 3 is Zone 4 and Zone 2, Type 4 is Zone 4 and Zone 5, Type 5 is Zone 3 and Zone 2, Type 8 is Zone 5 and unemployment/missing.

spell.dur: The duration of each of the spells presented above duration: The total time spent in each state These look pretty similar, though you can see how duration slightly preferences single state durations whereas spell.dur preferences subsequence durations

pattern: Count of the frequent subsequences of states in the distinct successive states AFpattern: Age at the first occurrence of the above frequent subsequence Pretty similar

transition: Count of the frequent subsequence of events in each sequence, where each transition is considered another event AFtransition: Age at the first occurrence of the above frequent subsequence These look pretty similar but the most different of AF pairs.

Complexity: Complexity index, number of transitions, turbulence These are interesting though maybe not as useful as others. I think Type 3 is really interesting, with a mid-career zone change, back to the original zone. I wonder if this may be more useful with less clusters.

Testing cluster quality

  • Point Biserial Correlation PBC [−1; 1] Max Measure of the capacity of the clustering to reproduce the distances.
  • Hubert’s Gamma HG [−1; 1] Max Measure of the capacity of the clustering to reproduce the distances (order of magnitude).
  • Hubert’s Somers’ D HGSD [−1; 1] Max Measure of the capacity of the clustering to reproduce the distances (order of magnitude) taking into account ties in distances.
  • Hubert’s C HC [0; 1] Min Gap between the partition obtained and the best partition theoretically possible with this number of groups and these distances.
  • Average Silhouette Width ASW [−1; 1] Max Coherence of assignments. High coherence indicates high between-group distances and strong within-group homogeneity. If this is weak, it means that the groups are not clearly separated or that the homogeneity of the groups is low.
  • Average Silhouette Width (weighted) ASWw [−1; 1] Max As previous, for floating point weights.
  • Calinski-Harabasz index CH [0; +∞[ Max Pseudo F computed from the distances.
  • Calinski-Harabasz index CHsq [0; +∞[ Max As previous, but using squared distances.
  • Pseudo R2 R2 [0; 1] Max Share of the discrepancy explained by the clustering solution (only to compare partitions with identical number of groups).

  • Pseudo R2 R2sq [0; 1] Max As previous, but using squared distances

  • ASW Interpretation proposed
    • 0.71 − 1.00 Strong structure identified.
    • 0.51 − 0.70 Reasonable structure identified.
    • 0.26 − 0.50 Structure is weak and could be artificial. Try other algorithms.
    • ≤ 0.25 No structure.
clusterpam_l$stats
wardRange <- as.clustrange(clusterward_l, diss = diss, ncluster = 20)
summary(wardRange, max.rank = 2)

numbers <- (2:20)
for (number in numbers) {
  clusterpam <- wcKMedoids(diss, k = number)
  assign(paste0("clusterpam_", number), clusterpam, envir = .GlobalEnv)
}

#pclustqual_AFpattern <- as.clustrange(clusterpropAFpattern, diss=diss, ncluster=8)
#pclustqual_AFtransition <- as.clustrange(clusterpropAFtransition, diss=diss, ncluster=8)
#pclustqual_Complexity <- as.clustrange(clusterpropComplexity, diss=diss, ncluster=8)
#pclustqual_duration <- as.clustrange(clusterpropduration, diss=diss, ncluster=8)
#pclustqual_pattern <- as.clustrange(clusterproppattern, diss=diss, ncluster=8)
#pclustqual_spell.age <- as.clustrange(clusterpropspell.age, diss=diss, ncluster=8)
#pclustqual_spell.dur <- as.clustrange(clusterpropspell.dur, diss=diss, ncluster=8)
#pclustqual_state <- as.clustrange(clusterpropstate, diss=diss, ncluster=8)
#pclustqual_transition <- as.clustrange(clusterproptransition, diss=diss, ncluster=8)

summary(pclustqual_AFpattern, max.rank = 2)
summary(pclustqual_AFtransition, max.rank = 2)
summary(pclustqual_Complexity, max.rank = 2)
summary(pclustqual_duration, max.rank = 2)
summary(pclustqual_pattern, max.rank = 2)
summary(pclustqual_spell.age, max.rank = 2)
summary(pclustqual_spell.dur, max.rank = 2)
summary(pclustqual_state, max.rank = 2)
summary(pclustqual_transition, max.rank = 2)

clusterpam_2$stats #0.24
clusterpam_3$stats #0.3
clusterpam_4$stats #0.34
clusterpam_5$stats #0.38
clusterpam_6$stats #0.28
clusterpam_7$stats #0.27
clusterpam_8$stats #0.26
clusterpam_9$stats #0.22
clusterpam_10$stats #0.19
clusterpam_11$stats #0.19
clusterpam_12$stats #0.18
clusterpam_13$stats #0.16
clusterpam_14$stats #0.16
clusterpam_15$stats #0.17
clusterpam_16$stats #0.17
clusterpam_17$stats #0.15
clusterpam_18$stats #0.15
clusterpam_19$stats #0.14
clusterpam_20$stats #0.15

#ASWs are all super low, the highest comes from Ward's at 0.28, but in the interpretation this is still a weak structure and could be artificial

wardRange$stats$ASW # Clusters about even
clusterpam_5$ASW # A few clusters greatly reduce ASW
pclustqual_state$stats$ASW

clusterpam_8 <- clusterpam_5$clustering
clusterpam_8_fac <- factor(clusterpam_8) #, labels = paste("Type", 1:8))

#clusterpam_8_fac <- factor(clusterpam_8_fac, levels = c("Type 2", "Type 8", "Type 3", "Type 7", "Type 4", "Type 5", "Type 1", "Type 6"))

p_plot <- seqIplot(large[,1:30], group = clusterpam_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "pam")

Normalized clustering

Using norm = TRUE in seqdist() arguments makes the distance insenstitive to differences in sequence length. It is sometimes recommended in the literature (TraMineR User's Guide p. 93, recommended with LCP).

# Normal clustering

diss_norm <- seqdist(large, method = "OM", indel = 1, sm = "TRATE", with.missing = TRUE, norm = TRUE)
diss <- seqdist(large, method = "OM", indel = 1, sm = "TRATE", with.missing = TRUE)

clusterward <- agnes(diss, diss = TRUE, method = "ward")
clusterpam <- wcKMedoids(diss, k = 8)

clusterward_norm <- agnes(diss_norm, diss = TRUE, method = "ward")
clusterpam_norm <- wcKMedoids(diss_norm, k = 8)


# no normalization
clusterward_8 <- cutree(clusterward, k = 8)
clusterward_8_fac <- factor(clusterward_8, labels = paste("Type", 1:8))

clusterpam_8 <- clusterpam$clustering
clusterpam_8_fac <- factor(clusterpam_8, labels = paste("Type", 1:8))

clusterpam_8_fac <- factor(clusterpam_8_fac, levels = c("Type 2", "Type 8", "Type 3", "Type 7", "Type 4", "Type 5", "Type 1", "Type 6"))

par(mfrow=c(1,3))
w_plot <- seqIplot(large[,1:30], group = clusterward_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "wards")

p_plot <- seqIplot(large[,1:30], group = clusterpam_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "pam")

seqlegend(large)

as.data.frame(clusterward_8_fac) %>%
  group_by(clusterward_8_fac) %>% summarise(n = n())
## # A tibble: 8 x 2
##   clusterward_8_fac     n
##   <fct>             <int>
## 1 Type 1              926
## 2 Type 2              610
## 3 Type 3              350
## 4 Type 4              588
## 5 Type 5              624
## 6 Type 6              493
## 7 Type 7              143
## 8 Type 8              266
as.data.frame(clusterpam_8_fac) %>%
  group_by(clusterpam_8_fac) %>% summarise(n = n()) 
## # A tibble: 8 x 2
##   clusterpam_8_fac     n
##   <fct>            <int>
## 1 Type 2             549
## 2 Type 8             857
## 3 Type 3             276
## 4 Type 7             339
## 5 Type 4             316
## 6 Type 5             417
## 7 Type 1             537
## 8 Type 6             709
# normalized

clusterward_8 <- cutree(clusterward_norm, k = 8)
clusterward_8_fac <- factor(clusterward_8, labels = paste("Type", 1:8))

clusterpam_8 <- clusterpam_norm$clustering
clusterpam_8_fac <- factor(clusterpam_8, labels = paste("Type", 1:8))

clusterpam_8_fac <- factor(clusterpam_8_fac, levels = c("Type 2", "Type 8", "Type 3", "Type 7", "Type 4", "Type 5", "Type 1", "Type 6"))

par(mfrow=c(1,3))

w_plot <- seqIplot(large[,1:30], group = clusterward_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "wards_norm")

p_plot <- seqIplot(large[,1:30], group = clusterpam_8_fac, border = NA, use.layout = TRUE, cols = 8, withlegend = F, sortv = "from.start", main = "pam_norm")

seqlegend(large)

as.data.frame(clusterward_8_fac) %>%
  group_by(clusterward_8_fac) %>% summarise(n = n())
## # A tibble: 8 x 2
##   clusterward_8_fac     n
##   <fct>             <int>
## 1 Type 1             1179
## 2 Type 2              390
## 3 Type 3              451
## 4 Type 4              495
## 5 Type 5              294
## 6 Type 6              405
## 7 Type 7              339
## 8 Type 8              447
as.data.frame(clusterpam_8_fac) %>%
  group_by(clusterpam_8_fac) %>% summarise(n = n()) 
## # A tibble: 8 x 2
##   clusterpam_8_fac     n
##   <fct>            <int>
## 1 Type 2             684
## 2 Type 8             328
## 3 Type 3             242
## 4 Type 7             401
## 5 Type 4             350
## 6 Type 5             576
## 7 Type 1             765
## 8 Type 6             654
wardRange <- as.clustrange(clusterward, diss = diss, ncluster = 8)
summary(wardRange, max.rank = 2)
##      1. N groups     1.  stat 2. N groups     2.  stat
## PBC            5    0.4941080           4    0.4620564
## HG             8    0.7008662           7    0.6906604
## HGSD           8    0.7007941           7    0.6905942
## ASW            5    0.3181933           4    0.2913926
## ASWw           5    0.3190216           4    0.2920733
## CH             2  686.2603540           3  577.5061767
## R2             8    0.4251463           7    0.4111132
## CHsq           5 1184.7471728           4 1151.1067808
## R2sq           8    0.6347516           7    0.6167882
## HC             5    0.1412368           8    0.1423484
wardRange <- as.clustrange(clusterward_norm, diss = diss, ncluster = 8)
summary(wardRange, max.rank = 2)
##      1. N groups     1.  stat 2. N groups    2.  stat
## PBC            7    0.4492873           6   0.4472834
## HG             8    0.6933109           7   0.6841754
## HGSD           8    0.6932572           7   0.6841311
## ASW            5    0.2761490           6   0.2670433
## ASWw           5    0.2769935           6   0.2680382
## CH             2  568.5849454           3 539.1685971
## R2             8    0.3937191           7   0.3769868
## CHsq           5 1043.7535227           6 989.2894168
## R2sq           8    0.5926509           7   0.5736949
## HC             8    0.1416807           7   0.1438160
clusterpam$stats
##          PBC           HG         HGSD          ASW         ASWw           CH 
##    0.4413393    0.7499126    0.7498305    0.2418608    0.2433430  486.2407504 
##           R2         CHsq         R2sq           HC 
##    0.4602258 1209.2725579    0.6795352    0.1230527
clusterpam_norm$stats
##          PBC           HG         HGSD          ASW         ASWw           CH 
##    0.5579611    0.8406808    0.8406692    0.2613676    0.2627770  455.4417560 
##           R2         CHsq         R2sq           HC 
##    0.4440183 1133.0985587    0.6652043    0.1038394

The differences aren't very pronounced in this comparison. Comparing the Ward's there do seem to be some differences in the clusters created, but only for the very low membership clusters. It is possible that normalization only makes a difference when classifying the border/fuzzy sequences.

The stats for the both the Ward's and PAM cluster solutions indicate that the normalized clusters are a bit lower quality. This makes sense because the normalization parameter inherently introduces clusters with less strong within-group homogeneity.